Vertical compression is a transformation that multiplies a function by a number between 0 and 1, shrinking all y-values in College Algebra. The graph keeps its basic shape, but its height gets smaller.
Vertical compression in College Algebra means multiplying every output of a function by a number between 0 and 1. If the original function is f(x), the compressed version is af(x) where 0 < a < 1. That makes the graph shorter in the vertical direction, so points move closer to the x-axis.
This transformation changes y-values, not x-values. That means the graph keeps the same x-intercepts, the same basic outline, and the same period if you are working with a periodic function. What changes is how tall the graph looks. A point like (2, 6) on f(x) would become (2, 3) if you multiply the function by 1/2.
The easiest way to picture it is as a vertical squeeze. The graph does not slide left or right, and it does not flip unless a negative sign is involved. It simply gets flatter. In many College Algebra problems, you compare the parent function to the transformed function and ask, “Did the y-values shrink by a factor?”
For exponential functions, vertical compression often appears as a smaller coefficient in front of the exponential expression. For example, y = 1/3(2^x) is a vertically compressed version of y = 2^x. The curve still grows, but its outputs are scaled down, so it stays closer to the x-axis for the same x-values.
A common mistake is mixing up vertical compression with horizontal compression. Vertical compression changes the outputs, so you multiply the whole function. Horizontal compression changes the input, so it shows up inside the function instead. If you know whether the change happens outside or inside the function, the transformation gets much easier to read.
Vertical compression shows up anywhere College Algebra asks you to read or build transformed graphs from a parent function. If you can spot it quickly, you can sketch graphs faster, compare equations, and explain how a coefficient changes the shape of a model.
It also connects directly to function behavior. For a quadratic, a vertical compression makes the parabola wider. For an exponential curve, it lowers the output values without changing the growth pattern itself. That difference matters when you are asked to describe what happens to range, intercepts, or overall shape.
This term is also useful when you move between an equation and a graph. If a problem says a graph has been compressed vertically by a factor of 1/4, you can write the new function as 1/4 f(x). If you see an equation with a fraction in front, you can predict the graph will look shorter than the parent function.
In assignment work, these problems often show up as graph matching, transform-the-parent-function questions, and short explanations of how a coefficient changes the graph. Knowing vertical compression gives you a quick way to justify your answer instead of guessing from the picture.
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view galleryVertical Stretch
Vertical stretch is the opposite move. Instead of shrinking y-values by a factor between 0 and 1, it makes them larger by multiplying the function by a number greater than 1. If you can tell stretch from compression, you can predict whether the graph gets taller or shorter before you even plot points.
Vertical Scaling
Vertical scaling is the broader idea that the outputs of a function are multiplied by a constant. Vertical compression and vertical stretch are both types of vertical scaling, just in different directions. In College Algebra, the trick is noticing whether the scaling factor is less than 1 or greater than 1.
Parent Function
The parent function is the starting graph you transform. Vertical compression is easiest to see by comparing the new graph to its parent, because the shape stays the same while the height changes. Many College Algebra questions ask you to identify how a graph changed from its parent function.
Range
Range tells you what output values a function can take. Vertical compression often changes the range because the y-values get pulled closer to the x-axis. The graph may still have the same x-values, but its lowest and highest outputs are smaller in magnitude.
A quiz or problem set might give you a graph and ask you to identify the transformation, or it may give you an equation like y = 1/2 f(x) and ask what happened to the parent function. You should say the graph was vertically compressed by a factor of 1/2, then describe how the y-values changed. If the function is exponential, you may also need to explain that the growth pattern stays the same while the outputs get smaller. On graphing questions, check whether the coefficient is outside the function, because that is the signal that the change is vertical. On multiple-choice items, a common distractor is horizontal compression, so look carefully at whether the factor multiplies the whole function or the input.
These two transformations are easy to mix up because both change the graph’s height. Vertical compression uses a factor between 0 and 1, so the graph gets shorter. Vertical stretch uses a factor greater than 1, so the graph gets taller. If the coefficient is a fraction, think compression. If it is bigger than 1, think stretch.
Vertical compression multiplies a function’s outputs by a factor between 0 and 1, which makes the graph shorter.
The x-values stay the same, so the graph keeps its basic shape and only the vertical size changes.
A coefficient outside the function tells you the transformation is vertical, not horizontal.
In College Algebra, vertical compression shows up often with parent functions, graph matching, and exponential equations.
If you see a fraction in front of a function, ask whether the y-values are being scaled down before you sketch.
Vertical compression in College Algebra is when you multiply a function by a number between 0 and 1, making all the y-values smaller. The graph keeps the same shape, but it looks shorter or flatter. It is a vertical transformation, so the change affects outputs, not inputs.
Look for a coefficient outside the function that is less than 1. That factor shrinks the y-values, so points move closer to the x-axis. If the graph looks squished downward while keeping the same x-values and shape, it is vertically compressed.
No. Vertical compression changes the outputs by multiplying the whole function. Horizontal compression changes the inputs and appears inside the function. That difference matters because the graph reacts in different directions depending on where the factor shows up.
It lowers every output value of the exponential graph without changing the basic growth pattern. For example, y = 1/2(2^x) is a compressed version of y = 2^x. The curve still grows, but it stays closer to the x-axis for the same x-values.